EyeDoc, I know this sounds way to obvious, but often overlooked for long exposures. Make sure your lens and filter are 100% spotless, or you’ll be removing spots in post. It happens all the time, but more dramatic due to the extended exposure time.
The thing to watch for also is the angle of the sun compared to the position to the ND filter if you are shooting in high-noon or broad daylight time. The cheap variable ND’s tens to create some cross-hatching effects when the sun is at certain angles in comparison to the front element of the filter.
Give the 10-stop a try, you may be surprised to see that even with a very small aperture, it can still let in a lot of light. I shot a skyline once using a B+W 10 stop and a Lee .9 Graduated ND at ISO 400 f/14 for 30″ turned out great.
The reason why such a need for so dark of a filter was the sun was reflecting off of a glass high-rise onto a Bay, basically double reflection.